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Systems of Conservation Laws 1 : (Record no. 33185)

000 -LEADER
fixed length control field	07741nam a22004693i 4500
001 - CONTROL NUMBER
control field	EBC143895
003 - CONTROL NUMBER IDENTIFIER
control field	MiAaPQ
005 - DATE AND TIME OF LATEST TRANSACTION
control field	20181121123430.0
006 - FIXED-LENGTH DATA ELEMENTS--ADDITIONAL MATERIAL CHARACTERISTICS--GENERAL INFORMATION
fixed length control field	m o d \|
007 - PHYSICAL DESCRIPTION FIXED FIELD--GENERAL INFORMATION
fixed length control field	cr cnu\|\|\|\|\|\|\|\|
008 - FIXED-LENGTH DATA ELEMENTS--GENERAL INFORMATION
fixed length control field	181113s1999 xx o \|\|\|\|0 eng d
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
International Standard Book Number	9780511151286
--	(electronic bk.)
020 ## - INTERNATIONAL STANDARD BOOK NUMBER
Cancelled/invalid ISBN	9780521582339
035 ## - SYSTEM CONTROL NUMBER
System control number	(MiAaPQ)EBC143895
035 ## - SYSTEM CONTROL NUMBER
System control number	(Au-PeEL)EBL143895
035 ## - SYSTEM CONTROL NUMBER
System control number	(CaPaEBR)ebr2000668
035 ## - SYSTEM CONTROL NUMBER
System control number	(CaONFJC)MIL41867
035 ## - SYSTEM CONTROL NUMBER
System control number	(OCoLC)437072430
040 ## - CATALOGING SOURCE
Original cataloging agency	MiAaPQ
Language of cataloging	eng
Description conventions	rda
--	pn
Transcribing agency	MiAaPQ
Modifying agency	MiAaPQ
050 #4 - LIBRARY OF CONGRESS CALL NUMBER
Classification number	QA377 .S46413 1999
082 0# - DEWEY DECIMAL CLASSIFICATION NUMBER
Classification number	515.353
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name	Serre, Denis.
245 10 - TITLE STATEMENT
Title	Systems of Conservation Laws 1 :
Remainder of title	Hyperbolicity, Entropies, Shock Waves.
264 #1 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Place of publication, distribution, etc	Cambridge :
Name of publisher, distributor, etc	Cambridge University Press,
Date of publication, distribution, etc	1999.
264 #4 - PUBLICATION, DISTRIBUTION, ETC. (IMPRINT)
Date of publication, distribution, etc	©1999.
300 ## - PHYSICAL DESCRIPTION
Extent	1 online resource (287 pages)
336 ## - CONTENT TYPE
Content type term	text
Content type code	txt
Source	rdacontent
337 ## - MEDIA TYPE
Media type term	computer
Media type code	c
Source	rdamedia
338 ## - CARRIER TYPE
Carrier type term	online resource
Carrier type code	cr
Source	rdacarrier
505 0# - FORMATTED CONTENTS NOTE
Formatted contents note	Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Acknowledgments -- Introduction -- 1 Some models -- 1.1 Gas dynamics in eulerian variables -- The law of a perfect gas -- The Euler equations -- The entropy -- Barotropic models -- 1.2 Gas dynamics in lagrangian variables -- Criticism of the change of variables -- 1.3 The equation of road traffic -- 1.4 Electromagnetism -- Maxwell's equations -- Plane waves -- 1.5 Magneto-hydrodynamics -- Plane waves in M.H.D. -- A simplified model of waves -- 1.6 Hyperelastic materials -- Strings and membranes -- 1.7 Singular limits of dispersive equations -- 1.8 Electrophoresis -- 2 Scalar equations in dimension d = 1 -- 2.1 Classical solutions of the Cauchy problem -- The linear case -- Non-linear case. The method of characteristics -- Blow-up in finite time -- 2.2 Weak solutions, non-uniqueness -- The Rankine-Hugoniot condition -- Non-uniqueness for the Cauchy problem -- 2.3 Entropy solutions, the Kružkov existence theorem -- Approximate solutions -- entropy inequalities -- Irreversibility -- Existence and uniqueness for the Cauchy problem -- Application: admissible discontinuities -- Piecewise smooth entropy solutions -- Oleinik's condition -- Shocks -- 2.4 The Riemann problem -- Self-similar solutions. Rarefactions -- The solution of the Riemann problem -- 2.5 The case of f convex. The Lax formula -- The Hamilton-Jacobi equation -- A dual formula to Lax's -- 2.6 Proof of Theorem 2.3.5: existence -- The approach by semi-groups -- Accretivity of A -- Passage to the limit -- The general case -- 2.7 Proof of Theorem 2.3.5: uniqueness -- An inequality for two entropy solutions -- Integration of the inequality (2.19) -- End of the proof of Proposition 2.3.6 -- 2.8 Comments -- Oleinik's inequality -- Initial datum with bounded total variation -- Uniqueness: the duality method -- 2.9 Exercises.
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note	3 Linear and quasi-linear systems -- 3.1 Linear hyperbolic systems -- Fourier analysis -- Geometric conditions of hyperbolicity -- Plane waves -- Exercises -- 3.2 Quasi-linear hyperbolic systems -- 3.3 Conservative systems -- 3.4 Entropies, convexity and hyperbolicity -- Physical systems -- Proof of theorem -- Exercises -- 3.5 Weak solutions and entropy solutions -- The Rankine-Hugoniot condition -- Reversibility -- 3.6 Local existence of smooth solutions -- Indications about the proof -- A priori estimate of… -- Proof of Lemma 3.6.2 -- Convergence of the iterative scheme -- 3.7 The wave equation -- Huygens' principle -- Conservation and decay -- 4 Dimension d = 1, the Riemann problem -- 4.1 Generalities on the Riemann problem -- 4.2 The Hugoniot locus -- Local description of the Hugoniot locus -- Exercises -- Some symmetric functions -- Proof of Theorem 4.2.1 -- 4.3 Shock waves -- Entropy balance -- Proof of Lemmas 4.3.2 and 4.3.3 -- Genuinely non-linear characteristic fields -- Exercise -- 4.4 Contact discontinuities -- Riemann invariants -- Exercises -- 4.5 Rarefaction waves. Wave curves -- Parametrisation of wave curves -- 4.6 Lax's theorem -- The form of the solution of the Riemann problem -- Local existence of the solution of the Riemann problem -- 4.7 The solution of the Riemann problem for the p-system -- Hypotheses -- Rarefaction waves -- Shocks -- Wave curves -- The solution of the Riemann problem -- 4.8 The solution of the Riemann problem for gas dynamics -- Hypotheses -- The rarefaction waves -- The shocks -- The 1-shock-waves -- The 3-shock-waves -- Parametrisation of shock curves -- Wave curves -- The solution of the Riemann problem -- The case of a perfect gas -- 4.9 Exercises -- 5 The Glimm scheme -- 5.1 Functions of bounded variation -- 5.2 Description of the scheme -- 5.3 Consistency -- 5.4 Convergence -- Compactness.
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note	Estimate of the error -- Conclusion -- Entropy inequalities -- 5.5 Stability -- Supplements apropos of the local Riemann problem -- A linear functional -- A quadratic functional -- The induction -- 5.6 The example of Nishida -- Hypotheses and theorem -- A distance in U -- Stability -- The isothermal model of gas dynamics -- 5.7 2 × 2 Systems with diminishing total variation -- Description -- Stability -- 5.8 Technical lemmas -- Proof of Lemma 5.5.2 -- Proof of Theorem 5.1.3 -- 5.9 Supplementary remarks -- Other numerical schemes -- The rich case -- 'Continuous' Glimm functional -- 5.10 Exercises -- 6 Second order perturbations -- 6.1 Dissipation by viscosity -- Non-dissipative case -- Dissipation or production of entropy -- Partially hyperbolic systems -- 6.2 Global existence in the strictly dissipative case -- Local existence in L -- Norms -- Hypotheses -- Estimate of the derivatives -- Proof of lemma -- Extension of the solution… -- Existence with a small diffusion -- 6.3 Smooth convergence as… -- The energy estimate -- Two most favourable cases -- Uniformity of the existence times -- 6.4 Scalar case. Accuracy of approximation -- Proof of the lemma -- Proof of Theorem 6.4.2 -- 6.5 Exercises -- 7 Viscosity profiles for shock waves -- 7.1 Typical example of a limit of viscosity solutions -- Profiles vs. Lax's entropy condition -- Profile vs. Lax's shock condition -- 7.2 Existence of the viscosity profile for a weak shock -- The scalar case -- The case of weak shocks with B = b(u)I -- Extensions of Theorem 7.2.1… -- 7.3 Profiles for gas dynamics -- Isentropic fluid with viscosity -- 7.4 Asymptotic stability -- Generalities on the stability of profiles -- The scalar case -- 7.5 Stability of the profile for a Lax shock -- Transport vs. diffusion -- Non-linear diffusion waves -- The rôle of the terms… -- Calculation of the diffusion waves.
505 8# - FORMATTED CONTENTS NOTE
Formatted contents note	Liu's theorem -- 7.6 Influence of the diffusion tensor -- Example: gas dynamics -- 7.7 Case of over-compressive shocks -- Example 7.7.2 -- Over-compressive shocks -- Instability of the over-compressive shock -- 7.8 Exercises -- Bibliography -- Index.
520 ## - SUMMARY, ETC.
Summary, etc	Graduate text on mathematical theory of conservation laws and partial differential equations.
588 ## - SOURCE OF DESCRIPTION NOTE
Source of description note	Description based on publisher supplied metadata and other sources.
590 ## - LOCAL NOTE (RLIN)
Local note	Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
650 #0 - SUBJECT ADDED ENTRY--TOPICAL TERM
Topical term or geographic name as entry element	Conservation laws (Mathematics).
655 #4 - INDEX TERM--GENRE/FORM
Genre/form data or focus term	Electronic books.
700 1# - ADDED ENTRY--PERSONAL NAME
Personal name	Sneddon, I. N.
776 08 - ADDITIONAL PHYSICAL FORM ENTRY
Display text	Print version:
Main entry heading	Serre, Denis
Title	Systems of Conservation Laws 1 : Hyperbolicity, Entropies, Shock Waves
Place, publisher, and date of publication	Cambridge : Cambridge University Press,c1999
International Standard Book Number	9780521582339
797 2# - LOCAL ADDED ENTRY--CORPORATE NAME (RLIN)
Corporate name or jurisdiction name as entry element	ProQuest (Firm)
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier	<a href="https://ebookcentral.proquest.com/lib/buse-ebooks/detail.action?docID=143895">https://ebookcentral.proquest.com/lib/buse-ebooks/detail.action?docID=143895</a>
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